In a wireless network with multiple interfering links, interference alignment (IA) is used. IA is a transmission scheme achieving linear sum capacity scaling with the number of data links, at high SNR. With IA, each transmitter designs the precoder to align the interference on the subspace of allowable interference dimension over the time, frequency or space dimension, where the dimension of interference at each receiver is smaller than the total number of interferers. Therefore, each receiver simply cancels interferers and acquires interference-free desired signal space using zero-forcing (ZF) receive filter.
Most of conventional research on IA is considered to achieve the maximum gain of IA using the infinite selectivity over symbol extensions, which is unrealistic in practical wireless networks. Therefore, the recent studies on MIMO IA focused on the design of IA precoder using a finite space dimension over one transmission slot, which is called MIMO constant channel.
The difficulties of IA in MIMO constant channel is to derive the closed form solution of the IA precoder. In other word, conventional interference alignment (IA) solution for achieving the optimal degrees of freedom (DoF) requires product of all cross link channel information since all precoders are coupled. These coupled condition requires channel matrix multiplication. If channel state information at transmitter is imperfect, inaccurate channel matrix multiplication arises error amplification due to summation and multiplication of error. Therefore, IA solution for achieving the optimal DoF may not be optimal in practical system. To avoid the product of channel matrices to get better performance and reduce feedback overhead, efficient IA method is needed.